Contents

Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official.[8] Guglielmo directed a trading post in Bugia, Algeria. Fibonacci travelled with him as a young boy, and it was in Bugia that he learned about the Hindu–Arabic numeral system.[12][3]

Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system, which unlike the Roman numerals used at the time, allowed easy calculation using a place-value system. In 1202, he completed the Liber Abaci (Book of Abacus or The Book of Calculation) which popularized Hindu–Arabic numerals in Europe.[3]

Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. In 1240, the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo)[13] by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens.[14]

The date of Fibonacci's death is not known, but it has been estimated to be between 1240[15] and 1250,[16] most likely in Pisa.

A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled with Latin numbers and Roman numerals and the value in Hindu-Arabic numerals.

In the Liber Abaci (1202), Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as the Hindu–Arabic numeral system.[17][18] The book advocated numeration with the digits 0–9 and place value. The book showed the practical use and value of the new Hindu-Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, and other applications. The book was well-received throughout educated Europe and had a profound impact on European thought. No copies of the 1202 edition are known to exist.[19]

The 1228 edition, first section introduces the Hindu-Arabic numeral system and compares the system with other systems, such as Roman numerals, and methods to convert the other numeral systems into Hindu-Arabic numerals. Replacing the Roman numeral system, its ancient Egyptian multiplication method, and using an abacus for calculations, with a Hindu-Arabic numeral system was an advance in making business calculations easier and faster, which led to the growth of banking and accounting in Europe.[20][21]

The second section explains the uses of Hindu-Arabic numerals in business, for example converting different currencies, and calculating profit and interest, which were important to the growing banking industry. The book also discusses irrational numbers and prime numbers.[19][20][21]

Liber Abaci posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century.[22][23][24][25]

In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" included today and began the sequence with 1, 1, 2 ... He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.[26][27] Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.

Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, 2002)[17]

Practica Geometriae (1220), a compendium of techniques in surveying, the measurement and partition of areas and volumes, and other topics in practical geometry (English translation by Barnabas Hughes, Springer, 2008).

^See the incipit of Flos: "Incipit flos Leonardi bigolli pisani..." (quoted in the MS Word document Sources in Recreational Mathematics: An Annotated Bibliography by David Singmaster, 18 March 2004 – emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."The basic meanings of "bigollo" appear to be "good-for-nothing" and "traveller" (so it could be translated by "vagrant", "vagabond" or "tramp"). A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of "Eight hundred years young"), which is also one of the connotations of the English word "wandering". The translation "the wanderer" in the quote above tries to combine the various connotations of the word "bigollo" in a single English word.